计算机代数语言与CASSDR系统

用计算机进行代数结构的化简,是计算机代数的一个重要课题。本文给出了一个新的代数结构化简的计算机代数系统ＣＡＳＳＤＲ。该系统由ＲＥＤＵＣＥ和Ｍａｔｈｅｍａｔｉｃａ组合而成,能从事初等函数的规范化简,并能解释许多特殊问题,可作为教学软件使用。     

CASSDR系统应用研究

计算机代数有着广泛的应用．文献[1]给出了一个新的系统CASSDR，它综合了现有计算机代数REDUCE软件和Mathematica软件的长处．本文用该系统处理求方程的代数解、解高次联立方程组和隐函数的求导，并帮助评价拟会函数的结果     

巧用平方差公式简化计算

平方差公式是初中代数的一个重要公式，很多竞赛题都可以应用这个公式进行简算．     

一种计算机代数系统的设计与实现

为利用计算机对数学表达式进行自动推理,实现自主可控的计算机代数系统,提出了基于抽象语法树模式匹配的计算机代数系统设计方法。在对计算机代数系统设计过程进行认知与分解的基础上建立了总体设计模型,并利用F#强大的函数式编程语言能力,快速实现解析器和表达式模式匹配,从而提高开发效率。通过设计一个可实现表达式化简、展开、求导、极限、泰勒级数和积分等功能的计算机代数系统,验证了该设计的准确性和有效性。     

MAPLE在简谐振动合成中的应用

MAPLE是一种集符号运算、数值计算、图形可视化和建模仿真等多功能于一体的计算机代数系统。本文介绍MAPLE对简谐振动合成曲线的可视化和动画仿真,不仅使物理教学课堂生动活跃,而且加深学生对物理概念规律的理解和掌握。     

CASSDR系统应用研究

计算机代数有着广泛的应用,文献[1]给出了一个新的系统CASSDR,它综合了现有计算机代数SEDUCE软件和Mathematica软件的长处,本文用该系统处理求方程的代数解,解高次联方程组和隐函数的求导,并帮助评价拟合函数的结果。     

逻辑函数的另一种化简方法--Q-M化简法

本针对当前多数数字电子电路教材中化简逻辑函数采用的代数化简法和卡诺图化简法，介绍一种适用于计算机分析和处理的逻辑函数的另一种化简方法，即Q—M化简法，也称为系统列表化简法。     

极简函数依赖集的研究

通过对最简的最小函数依赖集的研究,提出了极简函数依赖集的概念．同时,依据函数依赖与逻辑代数的等价性原理,设计了极简函数依赖集的算法,实际上这也是一种最小函数依赖集的算法．     

R0-代数的MP-滤子

R0-代数是基于系统研究形式演绎系统∫^*而提出的一类逻辑代数．本文证明了一个R0-代数的所有MP-滤子所成的集合分别构成一个Brouwer格、一个伪补分配格和一个Dedikind格．     

非线性耦合Ito系统新精确解的符号计算

利用最近引入的齐次平衡原理与新代数法的思想,借助于计算机代数系统Maple软件,得到了一个非线性耦合Ito系统的新孤子解、周期解。较以往一些常见的方法而言,该方法简洁而有效。     

Learning from comparison in algebra

Mastery of algebra is an important yet difficult milestone for students, suggesting the need for more effective teaching strategies in the algebra classroom. Learning by comparing worked-out examples of algebra problems may be one such strategy. Comparison is a powerful learning tool from cognitive science that has shown promising results in prior small-scale studies in mathematics classrooms. This study reports on a yearlong randomized controlled trial testing the effect of an Algebra I supplemental comparison curriculum on students’ mathematical knowledge. 141 Algebra I teachers were randomly assigned to either implement the comparison curriculum as a supplement to their regular curriculum or to be a ‘business as usual’ control. Use of the supplemental curriculum was much less frequent than requested for many teachers, and there was no main effect of condition on student achievement. However, greater use of the supplemental curriculum was associated with greater procedural student knowledge. These findings suggest a role for comparison in the algebra classroom but also the challenges of supporting teacher integration of new materials into the curriculum.     

Longitudinal algebra prediction for early versus later takers

Algebra I is a crucial course for middle and high school students for successful STEM-related coursework. A key issue is whether students should take Algebra I in Grade 8 versus Grade 9. Large-scale policy studies show conflicting results, and there are few (particularly longitudinal) individual difference studies. In the study, 53 students were assessed in Grade 6 on cognitive, numerosity, and mathematical skills, and then followed; 26 students took Algebra I in Grade 8, and the other 27 in Grade 9. Comparisons between groups at Grade 6 revealed gaps in some (but not all) cognitive skills and on mathematical competencies, but not on numerosity. By Algebra I, gaps in cognitive skills diminished, but gaps in mathematical skills remained constant. Gaps in algebra skills were also apparent, despite the age difference between groups. Results suggest that the additional year of instruction was not optimally tuned to pave the way for strong Algebra I performance.     

线性代数在数学建模中的应用

通过在线性代数教学中的经验,阐述了线性代数教学中引入实际应用问题的重要性,并且通过具体例题给出了线性代数在数学建模中的应用.     

格中模糊集的上、下近似算子

本文定义了格中模糊集合的上、下近似集合,讨论了格中全体模糊集合的集合F（L）上的上、下近似算子的性质,研究F（L）的代数结构,证明在一定条件下（F（L）∧,∨,,aprR,aprR）是一个Pawlak代数。     

谈初中代数的复习

初中代数是初中数学的主要内容之一，全面、系统地复习初中代数知识，使学生在中考中能够顺利过关，是每一个数学教师所关心的问题。在大力提倡素质教育的今天，教育观念要从应试教育转到素质教育上来，但素质教育并不等于取消考试制度。因此，复习仍然是当前必不可少的一个重要环节。     

周易宇宙代数学

1984年,中国著名哲学家冯友兰先生在致中国第一届《周易》学术研讨会的贺信中,提出了“周易是宇宙代数学”的命题。这一命题受到国内外易学界的普遍赞扬和认同。但是,冯先生却说不出周易宇宙代数学的代数符号和数值为何。20世纪90年代初,著名华裔数学家焦蔚芳先生建立起焦氏“周易宇宙代数学”理论体系。这一个理论体系基本上是成功的。这是焦先生对易学研究的重大贡献。本文的目的是想对焦氏“周易宇宙代数学”作一调整,使其更加丰富和精确。不当之处,请焦先生和易学界同仁批评、指正。     

Measuring conceptual understanding in randomised controlled trials: Can comparative judgement help?

An impediment to conducting high-quality quantitative research studies in education is the paucity of valid measures of learning gains. Studies often seek to investigate students’ deep, conceptual understanding yet many measures assess only surface, procedural understanding. One reason is that the development of validated measures of conceptual understanding is resource intensive and time consuming, and success is not guaranteed. We evaluated a novel and efficient technique, based on comparative judgement, for assessing conceptual understanding. We applied the technique to a randomised controlled trial in which students were taught simple algebra based on either the Grid Algebra or the MiGen software package. The participants were Year 5 students (N = 188) drawn from four primary schools who had not encountered algebra previously. An instrument from the literature (Concepts in Secondary Mathematics and Science: Algebra Scale) and a novel comparative judgement assessment were administered following the intervention. Students in the Grid Algebra condition outperformed those in the MiGen condition on both post-test measures. The comparative judgement technique performed similarly to the standard instrument but was far more efficient to design and implement. The technique can, in principle, be quickly applied to any target concept of interest. We conclude that comparative judgement is a valid, reliable and practical tool that could help to increase both the quantity and quality of quantitative research in education.     

代数美与提高学生的学习兴趣

在代数教学中如何提高学生的学习兴趣一直是代数教师们所关心的主要问题。本文在对代数美进行探讨的基础上,对在代数教学中如何利用代数学科本身的内在美以提高学生的学习兴趣进行了初步的探讨。我们认为这对于提高学生的学习兴趣是大有帮助的。     

关于矩阵运算的教学研究

矩阵是高等代数的重要研究对象,是高等代数中学习其他知识点的重要工具,学好矩阵是学好高等代数的前提条件。文章以矩阵运算的教学为例,将矩阵的运算与大家熟知的数的运算相类比,使学生更容易理解与掌握矩阵运算的相关知识。